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<a href="_lattice_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">//===========================================================================</span><span class="comment"></span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment">/*!</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment"> *</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="comment"> * \brief   Various functions for generating n-dimensional grids</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="comment"> *          (simplex-lattices).</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="comment"> *</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="comment"> *</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="comment"> * \author   Bjørn Bugge Grathwohl</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><span class="comment"> * \date     February 2017</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="comment"> *</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="comment"> * \par Copyright 1995-2017 Shark Development Team</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span><span class="comment"> *</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="comment"> * &lt;BR&gt;&lt;HR&gt;</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="comment"> * This file is part of Shark.</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="comment"> * &lt;https://shark-ml.github.io/Shark/&gt;</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="comment"> *</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="comment"> * Shark is free software: you can redistribute it and/or modify</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="comment"> * it under the terms of the GNU Lesser General Public License as published</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="comment"> * by the Free Software Foundation, either version 3 of the License, or</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="comment"> * (at your option) any later version.</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="comment"> *</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="comment"> * Shark is distributed in the hope that it will be useful,</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span><span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span><span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span><span class="comment"> * GNU Lesser General Public License for more details.</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span><span class="comment"> *</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span><span class="comment"> * You should have received a copy of the GNU Lesser General Public License</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span><span class="comment"> * along with Shark.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span><span class="comment"> *</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="comment"> */</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span><span class="comment">//===========================================================================</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span> </div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span><span class="preprocessor">#ifndef SHARK_ALGORITHMS_DIRECT_SEARCH_OPERATORS_LATTICE</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span><span class="preprocessor">#define SHARK_ALGORITHMS_DIRECT_SEARCH_OPERATORS_LATTICE</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span> </div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span><span class="preprocessor">#include &lt;<a class="code" href="_base_8h.html">shark/LinAlg/Base.h</a>&gt;</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span><span class="preprocessor">#include &lt;<a class="code" href="_metrics_8h.html">shark/LinAlg/Metrics.h</a>&gt;</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span><span class="preprocessor">#include &lt;<a class="code" href="_random_8h.html">shark/Core/Random.h</a>&gt;</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span> </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span><span class="preprocessor">#include &lt;numeric&gt;</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span> </div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceshark.html" title="AbstractMultiObjectiveOptimizer.">shark</a> {</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span> </div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span><span class="keyword">namespace </span>detail {</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span> </div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="comment">/*</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span><span class="comment"> * An n-dimensional point sums to &#39;s&#39; if the sum of the parts equal &#39;s&#39;,</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span><span class="comment"> * e.g. the point (x_0,x_1,x_2) sums to x_0+x_1+x+2 etc.  The number of</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span><span class="comment"> * n-dimensional points that sum to &#39;s&#39; is given by the formula &quot;N over K&quot; where</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span><span class="comment"> * N is n - 2 + s + 1 and K is s.</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span><span class="comment"> */</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>std::size_t sumlength(std::size_t <span class="keyword">const</span> n, std::size_t <span class="keyword">const</span> sum);</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span> </div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span><span class="keywordtype">void</span> pointLattice_helper(</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    UIntMatrix &amp; pointMatrix,</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    std::size_t <span class="keyword">const</span> rowidx,</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    std::size_t <span class="keyword">const</span> colidx,</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    std::size_t <span class="keyword">const</span> sum_rest);</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span><span class="comment"></span> </div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span><span class="comment">/// \brief A corner is a point where exactly one dimension is non-zero.</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span><span class="comment"></span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> Iterator&gt;</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span><span class="keywordtype">bool</span> isLatticeCorner(Iterator begin, Iterator end){</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>    std::size_t nonzero = 0;</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    <span class="keywordflow">for</span>(<span class="keyword">auto</span> iter = begin; iter != end; ++iter)</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    {</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <span class="keywordflow">if</span>(nonzero &gt; 1)</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>        {</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>        }</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        <span class="keywordflow">if</span>(*iter &gt; 0)</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>        {</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>            ++nonzero;</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>        }</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    }</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>    <span class="keywordflow">return</span> nonzero == 1;</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>}</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span> </div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>} <span class="comment">// namespace detail</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span> </div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span> </div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span> </div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span><span class="comment">/*</span></div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span><span class="comment"> * Sample points uniformly and uniquely from the simplex given in the matrix.</span></div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span><span class="comment"> * Corners are always included in the sampled point set (unless excplicitly</span></div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span><span class="comment"> * turned off with keep_corners set to false). The returned matrix will always</span></div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span><span class="comment"> * have n points or the same number of points as the original matrix if n is</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span><span class="comment"> * smaller.</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span><span class="comment"> */</span></div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> Matrix, <span class="keyword">typename</span> randomType = shark::random::rng_type&gt;</div>
<div class="foldopen" id="foldopen00090" data-start="{" data-end="}">
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"><a class="line" href="namespaceshark.html#a4ccee7396e4625bd05c53a87c7cd8df8">   90</a></span>Matrix <a class="code hl_function" href="namespaceshark.html#a4ccee7396e4625bd05c53a87c7cd8df8">sampleLatticeUniformly</a>(</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    randomType &amp; rng, Matrix <span class="keyword">const</span> &amp; matrix,</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    std::size_t <span class="keyword">const</span> n,</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    <span class="keywordtype">bool</span> <span class="keyword">const</span> keep_corners = <span class="keyword">true</span></div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>){</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>    <span class="comment">// No need to do all the below stuff if we&#39;re gonna grab it all anyway.</span></div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    <span class="keywordflow">if</span>(matrix.size1() &lt;= n){</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>        <span class="keywordflow">return</span> matrix;</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>    }</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>    Matrix sampledMatrix(n, matrix.size2());</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>    std::set&lt;std::size_t&gt; added_rows;</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <span class="comment">// First find all the corners and add them to our set of sampled points.</span></div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    <span class="keywordflow">if</span>(keep_corners){</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>        <span class="keywordflow">for</span>(std::size_t row = 0; row &lt; matrix.size1(); ++row){</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>            <span class="keywordflow">if</span>(detail::isLatticeCorner(matrix.major_begin(row), matrix.major_end(row))){</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>                added_rows.insert(row);</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>            }</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>        }</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    }</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    <span class="keywordflow">while</span>(added_rows.size() &lt; n){</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>        <span class="comment">// If we sample an existing index it doesn&#39;t alter the set.</span></div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>        added_rows.insert(<a class="code hl_function" href="namespaceshark_1_1random.html#aa64d4174eaf7111b03e0504eaa56b666" title="Draws a discrete number in {low,low+1,...,high} by drawing random numbers from rng.">random::discrete</a>(rng, std::size_t(0), matrix.size1() - 1));</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    }</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    std::size_t i = 0;</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    <span class="keywordflow">for</span>(std::size_t major_idx : added_rows)</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    {</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>        std::copy(</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>            matrix.major_begin(major_idx), matrix.major_end(major_idx),</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>            sampledMatrix.major_begin(i)</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>        );</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>        ++i;</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    }</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    <span class="keywordflow">return</span> sampledMatrix;</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>}</div>
</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span><span class="comment"></span> </div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span><span class="comment">/// \brief A preferred region in a lattice-sampled unit sphere.</span></div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span><span class="comment">///</span></div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span><span class="comment">/// A preferred region is a pair with a radius and a vector.  The intersection</span></div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span><span class="comment">/// of the vector and the unit sphere denotes the center of the preferred</span></div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span><span class="comment">/// region, and the radius denotes the radius of a sphere constructed such that</span></div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span><span class="comment">/// the center point (intersection of vector and unit sphere) is on its</span></div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span><span class="comment">/// periphery.  Points are then sampled on this smaller sphere and projected up</span></div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span><span class="comment">/// on the unit sphere, thus restricting the covered</span></div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span><span class="comment">/// segment/area/volume/hypervolume of the unit sphere.  See Figure 1 in</span></div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span><span class="comment">/// &quot;Evolutionary Many-objective Optimization of Hybrid Electric Vehicle</span></div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span><span class="comment">/// Control: From General Optimization to Preference Articulation&quot;</span></div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"><a class="line" href="namespaceshark.html#a8e65279a37185756281cefcc975b5aba">  136</a></span><span class="comment"></span><span class="keyword">typedef</span> std::pair&lt;double, RealVector&gt; <a class="code hl_typedef" href="namespaceshark.html#a8e65279a37185756281cefcc975b5aba" title="A preferred region in a lattice-sampled unit sphere.">Preference</a>;</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span><span class="comment"></span> </div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span><span class="comment">/// \brief Return a set of evenly spaced n-dimensional points on the unit sphere</span></div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span><span class="comment">/// clustered around the specified preference points.</span></div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"><a class="line" href="namespaceshark.html#ab9ca889b44ff9b2a2d1c5f362f37d72c">  140</a></span><span class="comment"></span>RealMatrix <a class="code hl_function" href="namespaceshark.html#ab9ca889b44ff9b2a2d1c5f362f37d72c" title="Return a set of evenly spaced n-dimensional points on the unit sphere clustered around the specified ...">preferenceAdjustedUnitVectors</a>(</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>    std::size_t <span class="keyword">const</span> n, </div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    std::size_t <span class="keyword">const</span> sum,</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>    std::vector&lt;Preference&gt; <span class="keyword">const</span> &amp; preferences);</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span><span class="comment"></span> </div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span><span class="comment">/// \brief Return a set of of evenly spaced n-dimensional points on the &quot;unit</span></div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span><span class="comment">/// simplex&quot; clustered around the specified preference points.</span></div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"><a class="line" href="namespaceshark.html#a7e64390f71770323ca0865a7329803a3">  147</a></span><span class="comment"></span>RealMatrix <a class="code hl_function" href="namespaceshark.html#a7e64390f71770323ca0865a7329803a3" title="Return a set of of evenly spaced n-dimensional points on the &quot;unit simplex&quot; clustered around the spec...">preferenceAdjustedWeightVectors</a>(</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>    std::size_t <span class="keyword">const</span> n,</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>    std::size_t <span class="keyword">const</span> sum,</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>    std::vector&lt;Preference&gt; <span class="keyword">const</span> &amp; preferences);</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span><span class="comment"></span> </div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span><span class="comment">///\brief  Computes the number of Ticks for a grid of a certain size</span></div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span><span class="comment">///</span></div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span><span class="comment">///</span></div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span><span class="comment">/// Computes the least number of ticks in each dimension required to make an</span></div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span><span class="comment">/// n-dimensional simplex grid at least as many points as a target number points.   </span></div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span><span class="comment">/// For example, the points in a two-dimensional</span></div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span><span class="comment">/// grid -- a line -- with size n are the points (0,n-1), (1,n-2), ... (n-1,0).</span></div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"><a class="line" href="namespaceshark.html#a415796eac968fb1da2a007f6393f0eef">  159</a></span><span class="comment"></span>std::size_t <a class="code hl_function" href="namespaceshark.html#a415796eac968fb1da2a007f6393f0eef" title="Computes the number of Ticks for a grid of a certain size.">computeOptimalLatticeTicks</a>(</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>    std::size_t <span class="keyword">const</span> n, std::size_t <span class="keyword">const</span> target_count</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>);</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span><span class="comment"></span> </div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span><span class="comment">/// \brief Returns a set of evenly spaced n-dimensional points on the &quot;unit simplex&quot;.</span></div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"><a class="line" href="namespaceshark.html#a145d0396e10232e70e89b24df2afdf2c">  164</a></span><span class="comment"></span>RealMatrix <a class="code hl_function" href="namespaceshark.html#a145d0396e10232e70e89b24df2afdf2c" title="Returns a set of evenly spaced n-dimensional points on the &quot;unit simplex&quot;.">weightLattice</a>(std::size_t <span class="keyword">const</span> n, std::size_t <span class="keyword">const</span> sum);</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span><span class="comment"></span> </div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span><span class="comment">/// \brief Return a set of evenly spaced n-dimensional points on the unit sphere.</span></div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"><a class="line" href="namespaceshark.html#af270d535e78a54515afc3761e20f61b1">  167</a></span><span class="comment"></span>RealMatrix <a class="code hl_function" href="namespaceshark.html#af270d535e78a54515afc3761e20f61b1" title="Return a set of evenly spaced n-dimensional points on the unit sphere.">unitVectorsOnLattice</a>(std::size_t <span class="keyword">const</span> n, std::size_t <span class="keyword">const</span> sum);</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span> </div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span><span class="comment">/*</span></div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span><span class="comment"> * Computes the pairwise euclidean distance between all row vectors in the</span></div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span><span class="comment"> * matrix and returns a matrix containing, for each row vector, the indices of</span></div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span><span class="comment"> * the &#39;n&#39; closest row vectors.</span></div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span><span class="comment"> */</span></div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> Matrix&gt;</div>
<div class="foldopen" id="foldopen00175" data-start="{" data-end="}">
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"><a class="line" href="namespaceshark.html#a1e8a1f01151560571e1f3618c5be8cd9">  175</a></span>UIntMatrix <a class="code hl_function" href="namespaceshark.html#a1e8a1f01151560571e1f3618c5be8cd9">computeClosestNeighbourIndicesOnLattice</a>(</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>    Matrix <span class="keyword">const</span> &amp; m, std::size_t <span class="keyword">const</span> n){</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>    <span class="keyword">const</span> RealMatrix distances = distanceSqr(m, m);</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>    UIntMatrix neighbourIndices(m.size1(), n);</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>    <span class="comment">// For each vector we are interested in indices of the t closest vectors.</span></div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>    <span class="keywordflow">for</span>(std::size_t i = 0; i &lt; m.size1(); ++i)</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>    {</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>        <span class="comment">// Make some indices we can sort.</span></div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>        std::vector&lt;std::size_t&gt; indices(distances.size2());</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>        std::iota(indices.begin(), indices.end(), 0);</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>        <span class="comment">// Sort indices by the distances.</span></div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>        std::sort(indices.begin(), indices.end(),</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>                  [&amp;](std::size_t a, std::size_t b)</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>                  {</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>                      return distances(i, a) &lt; distances(i, b);</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>                  });</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>        <span class="comment">// Copy the T closest indices into B.</span></div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>        std::copy_n(indices.begin(), n, neighbourIndices.major_begin(i));</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>    }</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>    <span class="keywordflow">return</span> neighbourIndices;</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>}</div>
</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span> </div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span> </div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>} <span class="comment">// namespace shark</span></div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span> </div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span><span class="preprocessor">#endif </span><span class="comment">// SHARK_ALGORITHMS_DIRECT_SEARCH_OPERATORS_LATTICE</span></div>
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